Surfaces

Kinsey, L. Christine

doi:10.1007/978-1-4612-0899-0_4

Cited by 9 publications

(10 citation statements)

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“…A 2D disk has Euler characteristic χ =1 (ref. 32 ), which dictates that any orientational pattern aligned to the perimeter should carry a topological charge of +1 (ref. 33 ).…”

Section: Resultsmentioning

confidence: 99%

Finite particle size drives defect-mediated domain structures in strongly confined colloidal liquid crystals

et al. 2016

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When liquid crystals are confined to finite volumes, the competition between the surface anchoring imposed by the boundaries and the intrinsic orientational symmetry-breaking of these materials gives rise to a host of intriguing phenomena involving topological defect structures. For synthetic molecular mesogens, like the ones used in liquid-crystal displays, these defect structures are independent of the size of the molecules and well described by continuum theories. In contrast, colloidal systems such as carbon nanotubes and biopolymers have micron-sized lengths, so continuum descriptions are expected to break down under strong confinement conditions. Here, we show, by a combination of computer simulations and experiments with virus particles in tailor-made disk- and annulus-shaped microchambers, that strong confinement of colloidal liquid crystals leads to novel defect-stabilized symmetrical domain structures. These finite-size effects point to a potential for designing optically active microstructures, exploiting the as yet unexplored regime of highly confined liquid crystals.

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“…A 2D disk has Euler characteristic χ =1 (ref. 32 ), which dictates that any orientational pattern aligned to the perimeter should carry a topological charge of +1 (ref. 33 ).…”

Section: Resultsmentioning

confidence: 99%

Finite particle size drives defect-mediated domain structures in strongly confined colloidal liquid crystals

et al. 2016

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“…Furthermore, our surface meshes are orientable, and homeomorphic to the sphere if their boundaries (holes) are filled by disks to make them closed surfaces. For such a surface having b boundaries, χ = 2 − b (Kinsey, 1993). If valence 3 vertices are assigned a characteristic index of +1/4, valence 5 vertices assigned an index of −1/4, and valence 6 vertices assigned an index of −1/2, then the sum of characteristic indices for all extraordinary vertices of the surface equals its Euler characteristic number.…”

Section: Discussionmentioning

confidence: 99%

A three-dimensional finite element model of human atrial anatomy: New methods for cubic Hermite meshes with extraordinary vertices

Gonzales

Sturgeon

Krishnamurthy

et al. 2013

Medical Image Analysis

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High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the “local-to-global” derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 millimeters, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology.

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“…The surfaceŠ may for example be the union of three smooth surfaces S j , S k , and S l , manifolds embedded in R 3 , such thatŠ = S j ∪ S k ∪ S l . We assume that S j , S k , and S l are orientable manifold surfaces, possibly with piecewise-smooth boundaries [2,22], and that their subsequent unionŠ also conforms to this same definition of a surface. Although this assumption may seem obvious, we explicitly state it for clarity.…”

Section: Introductionmentioning

confidence: 99%

“…We specify M as the pair M = (K , V ) where K defines the topology and V defines the geometry. We assume as withŠ that M is an orientable triangulated manifold surface, possibly with boundary [22]. The vertices V are samples ofŠ such that noise may corrupt these samples.…”

Section: Introductionmentioning

confidence: 99%

Normal Vector Voting: Crease Detection and Curvature Estimation on Large, Noisy Meshes

et al. 2002

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Surfaces

Cited by 9 publications

References 0 publications

Finite particle size drives defect-mediated domain structures in strongly confined colloidal liquid crystals

Finite particle size drives defect-mediated domain structures in strongly confined colloidal liquid crystals

A three-dimensional finite element model of human atrial anatomy: New methods for cubic Hermite meshes with extraordinary vertices

Normal Vector Voting: Crease Detection and Curvature Estimation on Large, Noisy Meshes

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